Find the product of the given complex number and its conjugate.
1/5+4i

-15.96

Step-by-step explanation:

A conjugate is a binomial with the sign inside changed. So the conjugate of (1/5 + 4i) is (1/5 - 4i)

Set the original and the conjugate next to each other and F.O.I.L. Multiply the first numbers of each binomial, the 1/5 and the 1/5 to get 1/25. This is the "F."

Multiply the outer members, the 1/5 and the 4i to get - 60i. This is the "O."

Multiply the inner  numbers  ( the + 4i and the 1/5) to get + 60i. This is the "I."

Multiply the positive 4i and the negative 4i to get 16i squared

The positive 60i and the negative 60i cancel each other out.

The i squared changes into - 1. This makes the 16 negative.

Add 1/25 to - 16 to get - 15.96

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: